Measurement exploratory data analysis

DEVICES = [
    'beaglebone-fan',
    'beaglebone-compressor',
    'beaglebone-pump',
    'beaglebone-refrigerator',
    'mafaulda-a',
    'mafaulda-b'
]

DEVICE = DEVICES[2]
T_WAVEFORM = 5  # (1 = MaufaulDa, 5 = others)
T_SEC = T_WAVEFORM
NFFT = 2**10   # (2**10 = MaufaulDa, 2**14 = others)
F_LIMIT = None # (3000 = MaufaulDa, None = others)

import os
import pandas as pd
import numpy as np
import matplotlib.pylab as plt

from tabulate import tabulate
from IPython.display import Markdown, HTML
from tqdm.notebook import tqdm

from typing import List, Tuple
from scipy.signal import find_peaks, butter, lfilter
from tsfel.feature_extraction.features import fundamental_frequency

from zipfile import ZipFile
import sys
sys.path.append('../')
from vibrodiagnostics import mafaulda, selection, discovery, models


def beaglebone_measurement(filename: str, fs: int) -> Tuple[str, pd.DataFrame]:
    g = 9.81
    milivolts = 1800
    resolution = 2**12
    columns = ['x', 'y', 'z']
    ts = pd.read_csv(filename, delimiter='\t', index_col=False, header=None, names=columns)
        
    # Calculate amplitude in m/s^2 Beaglebone Black ADC and ADXL335 resolution (VIN 1.8V, 12bits)
    for dim in columns:
        ts[dim] = ts[dim] * (milivolts / resolution)  # ADC to mV
        ts[dim] = (ts[dim] / 180) * g                 # mV to m/s^2 (180 mV/g)
        ts[dim] -= ts[dim].mean()

    ts['t'] = ts.index * (1 / fs)
    ts.set_index('t', inplace=True)
    return (os.path.basename(filename), ts, fs, ts.columns)  # last is feature columns


def beaglebone_dataset(filenames: List[str], fs: int) -> List[Tuple[str, pd.DataFrame]]:
    dataset = []
    for filename in filenames:
        name, ts, fs, cols = beaglebone_measurement(filename, fs)
        dataset.append((name, ts))
    return dataset


def lowpass_filter(data, cutpoint, fs, order=5):
    b, a = butter(order, cutpoint, fs=fs, btype='lowpass')
    y = lfilter(b, a, data)
    return y


def mafaulda_dataset(
        place=['ax', 'ay', 'az'],
        features_path =  '../../datasets/features_data/',
        mafaulda_path='../../datasets/MAFAULDA.zip',
        rpm=2500,
        lowpass_hz=10000):

    metadata_filename = os.path.join(features_path, selection.MAFAULDA_METADATA)
    faults = {
        'normal': 'normal',
        'imbalance': 'imbalance',
        'horizontal-misalignment': 'misalignment',
        'vertical-misalignment': 'misalignment',
        'overhang-cage_fault': 'cage fault',
        'underhang-cage_fault': 'cage fault',
        'underhang-ball_fault': 'ball fault',
        'overhang-ball_fault': 'ball fault',
        'overhang-outer_race': 'outer race fault',
        'underhang-outer_race': 'outer race fault',
    }

    metadata = pd.read_csv(metadata_filename, index_col='filename')
    metadata.reset_index(inplace=True)
    metadata = models.fault_labeling(metadata, faults)
    files = pd.DataFrame()
    # Worst severity and mid rpm
    for name, group in metadata[metadata['rpm'] >= rpm].groupby(by='fault', observed=False):
        files = pd.concat([
            files,
            group[
                group['severity_level'] == group['severity_level'].max()
            ].sort_values(by='rpm', ascending=True).head(1)
        ])
    ordering = {
        'normal': 0,
        'misalignment': 1,
        'imbalance': 2,
        'cage fault': 3,
        'ball fault': 4,
        'outer race fault': 5,
    }
    source = ZipFile(mafaulda_path)
    dataset = len(files) * [0]
    for index, file in files.iterrows():
        ts = mafaulda.csv_import(source, file['filename'])
        ts = ts[place]
        ts.columns = ts.columns.str.extract(r'(\w)$')[0]
        for axis in ts.columns:
            ts[axis] = lowpass_filter(ts[axis], lowpass_hz, file['fs'])
        pos = ordering[file['fault']]
        dataset[pos] = ((file['fault'] + ' (' + file['filename'] +')', ts))

    return dataset

Load dataset

if DEVICE == 'beaglebone-fan':
    Fs = 2500
    path = '../../inspections/fan/'
    files = [
        '1_still.tsv', '2_still.tsv', '3_still.tsv',
        '1_up.tsv', '2_up.tsv', '3_up.tsv',
        '1_down.tsv', '2_down.tsv', '3_down.tsv'
    ]
    files = [os.path.join(path, name) for name in files]
    DATASET = beaglebone_dataset(files, Fs)

elif DEVICE == 'beaglebone-compressor':
    Fs = 2500
    path = '../../inspections/datacentres/shc3/'
    files = [
        'k3_1.tsv', 'k3_2.tsv', 'k3_3.tsv', 'k3_4.tsv',
        'k5_1.tsv', 'k5_2.tsv', 'k5_3.tsv', 'k5_4.tsv'
    ]
    files = [os.path.join(path, name) for name in files]
    DATASET = beaglebone_dataset(files, Fs)

elif DEVICE == 'beaglebone-pump':
    Fs = 2500
    path = '../../inspections/bvs/'
    files = [
        'bvs_1_hore.tsv', 'bvs_2_hore.tsv' 
        #, 'bvs_3_motor.tsv', 'bvs_4_motor.tsv'
    ]    
    files = [os.path.join(path, name) for name in files]
    DATASET = beaglebone_dataset(files, Fs)

elif DEVICE == 'beaglebone-refrigerator':
    Fs = 2500
    path = '../../inspections/home-refrigerator/'
    files = [
        'ch1.tsv', 'ch2.tsv', 'ch3.tsv', 'ch4.tsv', 'ch5.tsv'
    ]    
    files = [os.path.join(path, name) for name in files]
    DATASET = beaglebone_dataset(files, Fs)

elif DEVICE == 'mafaulda-a':
    Fs = mafaulda.FS_HZ
    DATASET = mafaulda_dataset(place=['ax', 'ay', 'az'])

elif DEVICE == 'mafaulda-b':
    Fs = mafaulda.FS_HZ
    DATASET = mafaulda_dataset(place=['bx', 'by', 'bz'])

for name, ts in DATASET:
    display(Markdown(f'**{name}**'))
    ts.info()
    print()

bvs_1_hore.tsv

<class 'pandas.core.frame.DataFrame'>
Index: 76500 entries, 0.0 to 30.599600000000002
Data columns (total 3 columns):
 #   Column  Non-Null Count  Dtype  
---  ------  --------------  -----  
 0   x       76500 non-null  float64
 1   y       76500 non-null  float64
 2   z       76500 non-null  float64
dtypes: float64(3)
memory usage: 2.3 MB

bvs_2_hore.tsv

<class 'pandas.core.frame.DataFrame'>
Index: 51000 entries, 0.0 to 20.3996
Data columns (total 3 columns):
 #   Column  Non-Null Count  Dtype  
---  ------  --------------  -----  
 0   x       51000 non-null  float64
 1   y       51000 non-null  float64
 2   z       51000 non-null  float64
dtypes: float64(3)
memory usage: 1.6 MB

for name, ts in DATASET:
    display(Markdown(f'**{name}**'))
    display(tabulate(ts.describe(), headers='keys', tablefmt='html'))
    ts.boxplot(grid=True)
    plt.show()

bvs_1_hore.tsv

	x	y	z
count	76500	76500	76500
mean	4.55518e-15	1.23695e-14	3.69863e-15
std	0.39246	0.6742	0.483534
min	-1.53161	-2.60494	-1.96145
25%	-0.262246	-0.473369	-0.332838
50%	0.00120628	0.00563534	0.026415
75%	0.264658	0.460689	0.337768
max	1.70167	2.54436	1.70293

bvs_2_hore.tsv

	x	y	z
count	51000	51000	51000
mean	6.45201e-16	1.4482e-14	7.69991e-15
std	0.396248	0.674178	0.523105
min	-1.54745	-2.62487	-1.93246
25%	-0.278093	-0.469353	-0.375698
50%	-0.0146411	-0.0142992	0.00750486
75%	0.272761	0.464705	0.366758
max	1.66187	2.73997	2.21092

Statistical tests

• Normality test: Kolmogorov–Smirnov test
• Normality visual test: Quantile-quantile plot on chosen recording
• Stationarity test: Augmented Dickey–Fuller test
• Stationarity visual test: Autocorrelation plot

from statsmodels.tsa.stattools import adfuller
from statsmodels.api import qqplot
from scipy.stats import kstest

normality_tests = []
for name, ts in DATASET:
    for x in ts.columns:
        p_value = kstest(ts[x], 'norm').pvalue
        test = {'name': name, 'axis': x, 'p-value': p_value, 'not-normal': p_value < 0.05}
        normality_tests.append(test)

normality_tests = pd.DataFrame.from_records(normality_tests)
print(normality_tests.value_counts('not-normal'))
normality_tests.describe()

not-normal
True    6
Name: count, dtype: int64

	p-value
count	6.0
mean	0.0
std	0.0
min	0.0
25%	0.0
50%	0.0
75%	0.0
max	0.0

name, ts = DATASET[0]
fig, ax = plt.subplots(1, len(ts.columns), figsize=(10, 4))
for i, x in enumerate(ts.columns):
    qqplot(ts[x], line='45', ax=ax[i], marker='.', alpha=0.5)
    ax[i].set_title(f'Axis: {x}')

plt.tight_layout()
print(name)
plt.show()

bvs_1_hore.tsv

stationarity_tests = []
for name, ts in tqdm(DATASET):
    for x in ts.columns:
        result = adfuller(ts[x].loc[T_WAVEFORM:T_WAVEFORM+1])
        p_value = result[1]
        test = {
            'name': name,
            'axis': x,
            'statistic': result[0],
            'p-value': p_value,
            'stationary': p_value < 0.001
        }
        stationarity_tests.append(test)

stationarity_tests = pd.DataFrame.from_records(stationarity_tests)
print(stationarity_tests.value_counts('stationary'))
stationarity_tests['p-value'].describe()

  0%|          | 0/2 [00:00<?, ?it/s]

stationary
True    6
Name: count, dtype: int64

count    6.000000e+00
mean     4.328510e-17
std      1.050096e-16
min      3.730679e-25
25%      8.407889e-21
50%      4.863154e-20
75%      1.504009e-18
max      2.576292e-16
Name: p-value, dtype: float64

name, ts = DATASET[0]
fig, ax = plt.subplots(1, len(ts.columns), figsize=(10, 4))
for i, x in enumerate(ts.columns):
    ax[i].acorr(ts[x], maxlags=50)
    ax[i].set_title(f'Axis: {x}')

plt.tight_layout()
print(name)
plt.show()

bvs_1_hore.tsv

Time domain histogram

for name, ts in DATASET:
    display(Markdown(f'**{name}**'))
    axis = ts.columns
    ax = ts[axis].hist(figsize=(15, 3), grid=True, bins=100, layout=(1, 3), edgecolor='black', linewidth=0.5)
    plt.show()

bvs_1_hore.tsv

bvs_2_hore.tsv

Time domain waveform

for name, ts in DATASET:
    display(Markdown(f'**{name}**'))
    axis = ts.columns
    
    ax = ts[axis].plot(figsize=(20, 8), grid=True, subplots=True)
    for i, axname in enumerate(axis):
        ax[i].set_xlabel('Time [s]')
        ax[i].set_ylabel(f'Amplitude ({axname}) [m/s^2]')
    plt.show()               # plt.savefig('waveform.png')

bvs_1_hore.tsv

bvs_2_hore.tsv

Time domain waveform zoom detail

for name, ts in DATASET:
    axis = ts.columns
    display(Markdown(f'**{name}**'))
    ax = (ts[axis].iloc[int(T_WAVEFORM*Fs):int(T_WAVEFORM*Fs)+Fs]
                  .plot(figsize=(20, 10), grid=True, subplots=True))
    
    for i, axname in enumerate(axis):
        ax[i].set_xlabel('Time [s]')
        ax[i].set_ylabel(f'Amplitude ({axname}) [m/s^2]')
        plt.show()      # plt.savefig('waveform_zoom.png')

bvs_1_hore.tsv

bvs_2_hore.tsv

Time domain waveform zoom - faults side by side

fig, ax = plt.subplots(len(DATASET), 3, figsize=(12, 15), sharex=True)

for idx, df in enumerate(DATASET):
    name, ts = df
    columns = ts.columns
    ax[idx][1].set_title(name)
    ax[idx][0].set_ylabel('Amplitude [m/s^2]')

    for pos, axis in enumerate(columns):
        data = ts[axis].loc[T_WAVEFORM:T_WAVEFORM+0.3]
        ax[idx][pos].plot(data.index, data, linewidth=1, color='darkblue')
        ax[idx][pos].grid()
    

plt.tight_layout()
plt.show()

def spectogram(x, debug=True):
    fig, ax = plt.subplots(figsize=(15, 4))
    cmap = plt.get_cmap('inferno')
    pxx, freqs, t, im = plt.specgram(
        x, NFFT=NFFT, Fs=Fs,
        detrend='mean',
        mode='magnitude', scale='dB',
        cmap=cmap, vmin=-60
    )
    fig.colorbar(im, aspect=20, pad=0.04)
    ax.set_xlabel('Time [s]')
    ax.set_ylabel('Frequency [Hz]')
    mafaulda.resolution_calc(Fs, NFFT)
    return freqs, pxx


def window_idx(t):
    return (Fs * t) // NFFT + 1


def spectrum_slice(freqs, Pxx, t):
    fig, ax = plt.subplots(2, 1, figsize=(20, 8))
    n = window_idx(t)

    dB = 20 * np.log10(Pxx.T[n] / 0.000001)
    ax[0].plot(freqs, dB)      # 1 dB = 1 um/s^2
    ax[0].grid(True)
    ax[0].set_xlabel('Frequency [Hz]')
    ax[0].set_ylabel('Amplitude [dB]')
    
    ax[1].plot(freqs, Pxx.T[n])
    ax[1].grid(True)
    ax[1].set_xlabel('Frequency [Hz]')
    ax[1].set_ylabel('Amplitude [m/s^2]')
    return n


def get_max_frequency(freqs, Pxx, i):
    max_freq = freqs[np.argmax(Pxx.T[i])]
    return max_freq


def get_peaks(freqs, Pxx, i, top=5):
    amplitudes = Pxx.T[i]
    peaks, _ = find_peaks(amplitudes, distance=3)

    fundamental = get_max_frequency(freqs, Pxx, i)
    f_top = freqs[peaks[np.argsort(amplitudes[peaks])]][::-top]
    y_top = np.sort(amplitudes[peaks])[::-top]

    return pd.DataFrame({
        'f': f_top,
        'y': y_top,
        '1x': f_top / fundamental 
    })


def butter_bandpass_filter(data, lowcut, highcut, fs, order=5):
    b, a = butter(order, [lowcut, highcut], fs=fs, btype='band')
    y = lfilter(b, a, data)
    return y


def get_spectrograms(DATASET: List[pd.DataFrame], axis: str) -> list:
    spectrograms = []

    for name, ts in DATASET:
        base_freq = fundamental_frequency(ts[axis], Fs)
        display(Markdown(f'**{name}** *({axis.upper()} axis, Fundamental = {base_freq:.4f} Hz)*'))
        
        freqs, Pxx = spectogram(ts[axis])
        spectrograms.append((name, freqs, Pxx))
        plt.show()          # plt.savefig(f'x_axis_fft_{NFFT}.png')
    
    return spectrograms


def show_spectrogram_detail(spectrograms: list, axis: str, t: float):
    for name, freqs, Pxx in spectrograms:
        display(Markdown(f'**{name}** ({axis.upper()} axis @ {t}s)'))
        i_window = spectrum_slice(freqs, Pxx, t)
        plt.show()           #plt.savefig(f'x_axis_fft_{NFFT}_at_{T_SEC}s.png')


def show_mms_peaks(spectrograms: list, axis: str, t: float):
    for name, freqs, Pxx in spectrograms:
        display(Markdown(f'**{name}** ({axis.upper()} axis @ {t}s)'))
    
        i_window = window_idx(t)
        peaks = discovery.mms_peak_finder(Pxx.T[i_window])
        
        fig, ax = plt.subplots(1, 1, figsize=(15, 3))
        ax.grid(True)
        ax.plot(freqs, Pxx.T[i_window])
        ax.scatter(freqs[peaks], Pxx.T[i_window][peaks], marker='^', color='red')
        ax.set_xlabel('Frequency [Hz]')
        
        plt.show()


def show_harmonic_series(spectrograms: list, axis: str, t: float):
    # https://stackoverflow.com/questions/1982770/changing-the-color-of-an-axis
    for name, freqs, Pxx in spectrograms:
        display(Markdown(f'**{name}** ({axis.upper()} axis @ {t}s)'))
    
        i_window = window_idx(t)
        h_series = discovery.harmonic_series_detection(freqs, Pxx.T[i_window], Fs, NFFT)
    
        # Find best (sum of harmonics' amplitudes in the largest)
        max_harmonic_amp_idx = np.argmax([
            sum([h[1] for h in s]) / len(s)
            for s in h_series
        ])
        best_harmonic_series = pd.DataFrame(
            h_series[max_harmonic_amp_idx],
            columns=['Frequency [Hz]', 'Amplitude [m/s^2]']
        )
        best_harmonic_series.index += 1
        display(tabulate(best_harmonic_series, headers='keys', tablefmt='html'))
    
        # Plot found harmonic series
        fig, ax = plt.subplots(1, 8, figsize=(30, 4))
        for i in range(8):
            s = h_series[i+1]
            if i == max_harmonic_amp_idx:
                ax[i].xaxis.label.set_color('red')
    
            ax[i].plot(freqs, Pxx.T[i_window])
            ax[i].scatter([x[0] for x in s], [x[1] for x in s], marker='^', color='red')
            ax[i].set_xlabel('Frequency [Hz]')
    
        plt.show()

def show_spectra_largest_amplitudes(spectrograms: list, axis: str, t: float):
    for name, freqs, Pxx in spectrograms:
        display(Markdown(f'**{name}** ({axis.upper()} axis @ {t}s)'))

        i_window = window_idx(t)
        x_fundamental = get_max_frequency(freqs, Pxx, i_window)
        peaks = get_peaks(freqs, Pxx, i_window)
        
        display(Markdown(f'- *Fundamental frequency:* {x_fundamental} Hz'))
        display(tabulate(peaks.head(5), headers='keys', tablefmt='html'))


def compare_limited_specrograms(spectrograms: list, axis: str, t: float):
    fig, ax = plt.subplots(len(DATASET), 1, figsize=(20, 20), sharey=True)
    i = 0
    for name, ts in DATASET:
        signal = ts[axis].loc[t:t+NFFT/Fs].to_numpy()
        pxx = np.abs(np.fft.rfft(signal) / len(signal)) 
        freqs = np.fft.fftfreq(len(signal), d=1/Fs)[:len(pxx)]
        #ilast = len(freqs[freqs < F_LIMIT])
        
        ax[i].plot(freqs, pxx)
        ax[i].grid(True)
        ax[i].set_xlabel('Frequency [Hz]')
        ax[i].set_ylabel('Amplitude [m/s^2]')
        ax[i].set_xlim(0, F_LIMIT)
        ax[i].set_ylim(0, 0.4)
        ax[i].set_title(name)
        i += 1


def spectrogram_energy_left_cumulative(spectrograms: list, axis: str, t: float):
    fig, ax = plt.subplots(len(DATASET), 1, figsize=(20, 20), sharey=True)
    i = 0
    for name, ts in DATASET:
        signal = ts[axis].loc[t:t+NFFT/Fs].to_numpy()
        pxx = np.abs(np.fft.rfft(signal) / len(signal)) 
        freqs = np.fft.fftfreq(len(signal), d=1/Fs)[:len(pxx)]
        
        ax[i].plot(freqs, np.cumsum(pxx) / np.sum(pxx))
        ax[i].grid(True)
        ax[i].set_xlabel('Frequency [Hz]')
        ax[i].set_ylabel('Cumulative energy [%]')
        #ax[i].set_xlim(0, 10000)
        ax[i].set_title(name)
        i += 1

Compare mafaulda faults

compare_limited_specrograms(DATASET, 'x', T_SEC)
plt.tight_layout()
plt.show()

compare_limited_specrograms(DATASET, 'y', T_SEC)
plt.tight_layout()
plt.show()

compare_limited_specrograms(DATASET, 'z', T_SEC)
plt.tight_layout()
plt.show()

Compare cumulative sums

spectrogram_energy_left_cumulative(DATASET, 'x', T_SEC)
plt.tight_layout()
plt.show()

spectrogram_energy_left_cumulative(DATASET, 'y', T_SEC)
plt.tight_layout()
plt.show()

spectrogram_energy_left_cumulative(DATASET, 'z', T_SEC)
plt.tight_layout()
plt.show()

Spectrogram in X axis

x_spectra = get_spectrograms(DATASET, 'x')

bvs_1_hore.tsv (X axis, Fundamental = 24.3791 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

bvs_2_hore.tsv (X axis, Fundamental = 24.3627 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

Spectrogram detail in X axis

show_spectrogram_detail(x_spectra, 'x', T_SEC)

bvs_1_hore.tsv (X axis @ 5s)

bvs_2_hore.tsv (X axis @ 5s)

Peaks in frequency spectrum in X axis

• MMS peak finder algorithm

show_mms_peaks(x_spectra, 'x', T_SEC)

bvs_1_hore.tsv (X axis @ 5s)

bvs_2_hore.tsv (X axis @ 5s)

Harmonic series detection in X axis

# show_harmonic_series(x_spectra, 'x', T_SEC)

show_spectra_largest_amplitudes(x_spectra, 'x', T_SEC)

bvs_1_hore.tsv (X axis @ 5s)

• Fundamental frequency: 63.4765625 Hz

	f	y	1x
0	63.4766	0.113014	1
1	85.4492	0.0379399	1.34615
2	129.395	0.0272333	2.03846
3	593.262	0.0227783	9.34615
4	541.992	0.0186733	8.53846

bvs_2_hore.tsv (X axis @ 5s)

• Fundamental frequency: 61.03515625 Hz

	f	y	1x
0	61.0352	0.0873599	1
1	146.484	0.0349362	2.4
2	100.098	0.0218704	1.64
3	183.105	0.0201232	3
4	1098.63	0.0173606	18

Spectrogram in Y axis

y_spectra = get_spectrograms(DATASET, 'y')

bvs_1_hore.tsv (Y axis, Fundamental = 24.3791 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

bvs_2_hore.tsv (Y axis, Fundamental = 24.3627 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

Spectrogram detail in Y axis

show_spectrogram_detail(y_spectra, 'y', T_SEC)

bvs_1_hore.tsv (Y axis @ 5s)

bvs_2_hore.tsv (Y axis @ 5s)

Peaks in frequency spectrum in Y axis

show_mms_peaks(y_spectra, 'y', T_SEC)

bvs_1_hore.tsv (Y axis @ 5s)

bvs_2_hore.tsv (Y axis @ 5s)

Harmonic series detection in Y axis

# show_harmonic_series(y_spectra, 'y', T_SEC)

show_spectra_largest_amplitudes(y_spectra, 'y', T_SEC)

bvs_1_hore.tsv (Y axis @ 5s)

• Fundamental frequency: 24.4140625 Hz

	f	y	1x
0	24.4141	0.252131	1
1	468.75	0.0660276	19.2
2	593.262	0.056911	24.3
3	402.832	0.0511265	16.5
4	603.027	0.0443939	24.7

bvs_2_hore.tsv (Y axis @ 5s)

• Fundamental frequency: 24.4140625 Hz

	f	y	1x
0	24.4141	0.244484	1
1	583.496	0.0807483	23.9
2	405.273	0.054666	16.6
3	646.973	0.0454914	26.5
4	678.711	0.0403614	27.8

Spectrogram in Z axis

z_spectra = get_spectrograms(DATASET, 'z')

bvs_1_hore.tsv (Z axis, Fundamental = 24.3791 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

bvs_2_hore.tsv (Z axis, Fundamental = 24.3627 Hz)

Window size: 1024
Heinsenberg box
	Time step: 409.6 ms
	Frequency step: 2.44140625 Hz

Spectrogram detail in Z axis

show_spectrogram_detail(z_spectra, 'z', T_SEC)

bvs_1_hore.tsv (Z axis @ 5s)

bvs_2_hore.tsv (Z axis @ 5s)

Peaks in frequency spectrum in Z axis

show_mms_peaks(z_spectra, 'z', T_SEC)

bvs_1_hore.tsv (Z axis @ 5s)

bvs_2_hore.tsv (Z axis @ 5s)

Harmonic series detection in Z axis

# show_harmonic_series(z_spectra, 'z', T_SEC)

show_spectra_largest_amplitudes(z_spectra, 'z', T_SEC)

bvs_1_hore.tsv (Z axis @ 5s)

• Fundamental frequency: 24.4140625 Hz

	f	y	1x
0	24.4141	0.216447	1
1	73.2422	0.0392826	3
2	90.332	0.0297253	3.7
3	195.312	0.0224701	8
4	798.34	0.0184405	32.7

bvs_2_hore.tsv (Z axis @ 5s)

• Fundamental frequency: 24.4140625 Hz

	f	y	1x
0	24.4141	0.219855	1
1	58.5938	0.0495791	2.4
2	109.863	0.0368702	4.5
3	324.707	0.0300992	13.3
4	393.066	0.0230425	16.1

Histogram

axis = ['x', 'y', 'z']
for name, ts in DATASET:
    display(Markdown(f'**{name}**'))
    ts[axis].hist(figsize=(10, 5), grid=True, bins=50)
    plt.show()

bvs_1_hore.tsv

bvs_2_hore.tsv

axis = ['x', 'y', 'z']
for name, ts in DATASET:
    display(Markdown(f'**{name}**'))
    ts[axis].boxplot(figsize=(10, 5))
    plt.show()

bvs_1_hore.tsv

bvs_2_hore.tsv

Orbitals of all cross sections

for name, ts in DATASET:
    display(Markdown(f'**{name}**'))
    fig, ax = plt.subplots(1, 3, figsize=(20, 4))

    for i, col in enumerate([('x', 'y'), ('x', 'z'), ('y', 'z')]):
        ax[i].scatter(ts[col[0]], ts[col[1]], s=1)
        ax[i].grid(True)
        ax[i].set_xlabel(col[0].upper())
        ax[i].set_ylabel(col[1].upper())
        ax[i].grid(True)
    plt.show()       # plt.savefig('orbitals.png')

bvs_1_hore.tsv

bvs_2_hore.tsv

Orbitals of 1x harmonic frequency

x_spectra_by_name = {spec[0]: spec for spec in x_spectra}
y_spectra_by_name = {spec[0]: spec for spec in y_spectra}
z_spectra_by_name = {spec[0]: spec for spec in z_spectra}
t = 5
space = 5

for name, ts in DATASET:
    display(Markdown(f'**{name}**'))
    fig, ax = plt.subplots(1, 3, figsize=(20, 4))

    name, freqs, Pxx = x_spectra_by_name[name]
    x_fundamental = get_max_frequency(freqs, Pxx, window_idx(t))
    name, freqs, Pxx = y_spectra_by_name[name]
    y_fundamental = get_max_frequency(freqs, Pxx, window_idx(t))

    name, freqs, Pxx = z_spectra_by_name[name]
    z_fundamental = get_max_frequency(freqs, Pxx, window_idx(t))

    try:
        ts['x_1x'] = butter_bandpass_filter(ts['x'], x_fundamental - space, x_fundamental + space, Fs)
        ts['y_1x'] = butter_bandpass_filter(ts['y'], y_fundamental - space, y_fundamental + space, Fs)
        ts['z_1x'] = butter_bandpass_filter(ts['z'], z_fundamental - space, z_fundamental + space, Fs)
    except ValueError:
        continue
    
    for i, col in enumerate([('x_1x', 'y_1x'), ('x_1x', 'z_1x'), ('y_1x', 'z_1x')]):
        ax[i].scatter(ts[col[0]], ts[col[1]], s=1)
        ax[i].grid(True)
        ax[i].set_xlabel(col[0].upper())
        ax[i].set_ylabel(col[1].upper())
        ax[i].grid(True)
    
    plt.show()       # plt.savefig('orbitals_1x.png')

bvs_1_hore.tsv

bvs_2_hore.tsv

t = 5
space = 8

for name, ts in DATASET:
    display(Markdown(f'**{name}**'))

    name, freqs, Pxx = x_spectra_by_name[name]
    x_fundamental = get_max_frequency(freqs, Pxx, window_idx(t))
    name, freqs, Pxx = y_spectra_by_name[name]
    y_fundamental = get_max_frequency(freqs, Pxx, window_idx(t))

    name, freqs, Pxx = z_spectra_by_name[name]
    z_fundamental = get_max_frequency(freqs, Pxx, window_idx(t))

    try:
        x = butter_bandpass_filter(ts['x'], x_fundamental - space, x_fundamental + space, Fs)
        y = butter_bandpass_filter(ts['y'], y_fundamental - space, y_fundamental + space, Fs)
        z = butter_bandpass_filter(ts['z'], z_fundamental - space, z_fundamental + space, Fs)
    except ValueError:
        continue

    ax = plt.figure().add_subplot(projection='3d')
    ax.scatter(x, y, z, zdir='z', s=1, color='navy')
    ax.set_xlabel('x')
    ax.set_ylabel('y')
    ax.set_zlabel('z')
    ax.set_xlim(-2, 2)
    ax.set_ylim(-2, 2)
    ax.set_zlim(-2, 2)
    ax.zaxis.labelpad = -0.7
    plt.show()

bvs_1_hore.tsv

bvs_2_hore.tsv